[creatonez]

A good solution: for each language option, include both the exonym (name of the language in the user's currently selected language) and the endonym (name of the language in that particular language). Make sure the search feature can fuzzy match either field.

And yes, do not include any icons whatsoever. Text only. A standard for visual depiction of languages is not going to come any time soon, and flags are completely unsuitable for the purpose.